Frank Harary

Frank Harary (March 11, 1921 – January 4, 2005) was an American mathematician, who specialized in graph theory.

He was widely recognized as one of the "fathers" of modern graph theory.

Harary was a master of clear exposition and, together with his many doctoral students, he standardized the terminology of graphs.

He broadened the reach of this field to include physics, psychology, sociology, and even anthropology.

Gifted with a keen sense of humor, Harary challenged and entertained audiences at all levels of mathematical sophistication.

A particular trick he employed was to turn theorems into games—for instance, students would try to add red edges to a graph on six vertices in order to create a red triangle, while another group of students tried to add edges to create a blue triangle (and each edge of the graph had to be either blue or red).

Because of the theorem on friends and strangers, one team or the other would have to win.

Frank Harary was born in New York City, the oldest child to a family of Jewish immigrants from Syria and Russia.

He earned his bachelor's and master's degrees from Brooklyn College in 1941 and 1945 respectively and his Ph.D., with supervisor Alfred L. Foster, from University of California, Berkeley in 1948.

Prior to his teaching career he became a research assistant in the Institute of Social Research at the University of Michigan.

This article was first submitted to the American Mathematical Society in November 1948, then sent to the Duke Mathematical Journal where it was revised three times before it was finally published two years after its initial submission.

In 1949 Harary published On the algebraic structure of knots.

Harary's first publication, "Atomic Boolean-like rings with finite radical", went through much effort to be put into the Duke Mathematical Journal in 1950.

Harary began his teaching career at the University of Michigan in 1953 where he was first an assistant professor, then in 1959 associate professor and in 1964 was appointed as a professor of mathematics, a position he held until 1986.

Shortly after this publication in 1953 Harary published his first book (jointly with George Uhlenbeck) On the number of Husimi trees.

It was following this text that he began to build up a worldwide reputation for his work in graph theory.

In 1965 his first book Structural models: An introduction to the theory of directed graphs was published, and for the rest of his life his interest would be in the field of graph theory.

While beginning his work in graph theory around 1965, Harary began buying property in Ann Arbor, and subdividing the houses he bought into apartments.

This led to criticism for poor maintenance, "scores of building code violations", and six condemnations of buildings he owned.

In a 1969 newspaper article, Harary was quoted as stating "We just wanted these properties for the land value ... we wanted to move the tenants out", while his wife Jayne stated "We've wanted to help poor blacks find better housing, but we've taken the rap again and again."

Harary and his wife Jayne had six children together, Miriam, Natalie, Judith, Thomas, Joel and Chaya.

From 1973 to 2007 Harary jointly wrote five more books, each in the field of graph theory.

In the time before his death, Harary traveled the world researching and publishing over 800 papers (with some 300 different co-authors), in mathematical journals and other scientific publications, more than any mathematician other than Paul Erdos.

Harary recorded that he lectured in 166 different cities around the United States and some 274 cities in over 80 different countries.

Harary was particularly proud that he had given lectures in cities around the world beginning with every letter of the alphabet, even including "X" when he traveled to Xanten, Germany.

Harary also played a curious role in the award-winning film Good Will Hunting.

The film displayed formulas he had published on the enumeration of trees, which were supposed to be fiendishly difficult.

It was in 1986 at the age of 65 that Harary retired from his professorship at the University of Michigan.

Harary did not take his retirement lightly however; following his retirement Harary was appointed as a Distinguished Professor of Computer Sciences at New Mexico State University in Las Cruces.

From 1987 he was Professor (and Distinguished Professor Emeritus) in the Computer Science Department at New Mexico State University in Las Cruces.

He was one of the founders of the Journal of Combinatorial Theory and the Journal of Graph Theory.

He held this position until his death in 2005.

The same year as his retirement Harary was made an honorary fellow of the National Academy of Sciences of India; he also served as an editor for about 20 different journals focusing primarily on graph theory and combinatorial theory.

It was following his retirement that Harary was elected as an honorary lifetime member of the Calcutta Mathematical Society and of the South African Mathematical Society.

He died at Memorial Medical Center in Las Cruces, New Mexico.

At the time of his death in Las Cruces other members of the department of Computer Science felt the loss for the great mind that once worked beside them.

The head of the department of Computer Science at the time of Harary's death Desh Ranjan had this to say, "Dr. Harary was a true scholar with a genuine love for graph theory which was an endless source of new discoveries, beauty, curiosity, surprises and joy for him till the very end of his life."

Harary's work in graph theory was diverse.

Some topics of great interest to him were:

Among over 700 scholarly articles Harary wrote, two were co-authored with Paul Erdős, giving Harary an Erdős number of 1.